how do I put the 3D cursor inside an object?
Press Space and select Add Empty then Plain Axes, or add any other dummy object to your scene. Move the Empty object to your desired location using the usual G command. Then bring up the Snap menu with Shift+S and select Cursor to Selected (with access key u). Finally, press Delete to remove the Empty object.



The other techniques described in the comments (zooming in, being in wireframe mode and using Shift+S with Cursor to Grid) are quicker, whereas this technique gives you more precision.

Alternatively, you can press N to bring up the Properties pane, and manually adjust the 3D Cursor's X, Y and Z coordinates: